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On Estimates of Transition Density for Subordinate Brownian Motions with Gaussian Components in C1,1-open Sets

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Abstract

We consider a subordinate Brownian motion X with Gaussian components when the scaling order of purely discontinuous part is between 0 and 2 including 2. In this paper we establish sharp two-sided bounds for transition density of X in \({\mathbb {R}}^{d}\) and C1,1-open sets. As a corollary, we obtain a sharp Green function estimates.

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Acknowledgments

We are grateful to the referee for suggesting a short proof of Lemma 2.4.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    Joohak Bae

  2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Building 27, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826, Republic of Korea

    Panki Kim

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  1. Joohak Bae
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  2. Panki Kim
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Correspondence to Panki Kim.

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Joohak Bae was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. NRF-2015R1A4A1041675).

Panki Kim was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIP) (No. 2016R1E1A1A01941893).

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Bae, J., Kim, P. On Estimates of Transition Density for Subordinate Brownian Motions with Gaussian Components in C1,1-open Sets. Potential Anal 52, 661–687 (2020). https://doi.org/10.1007/s11118-018-9755-x

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